Tài liệu SEC 13 pptx

XIII NonlinearandFractal SignalProcessing AlanV.Oppenheim MassachusettsInstituteofTechnology GregoryW.Wor nell MassachusettsInstituteofTechnology 71ChaoticSignalsandSignalProcessing AlanV.OppenheimandKevinM.Cuomo Introduction • ModelingandRepresentationofChaoticSignals • EstimationandDetection • Use ofChaoticSignalsinCommunications • SynthesizingSelf-SynchronizingChaoticSystems 72NonlinearMaps StevenH.IsabelleandGregoryW.Wornell Introduction • EventuallyExpandingMapsandMarkovMaps • SignalsFromEventuallyExpanding Maps • EstimatingChaoticSignalsinNoise • ProbabilisticPropertiesofChaoticMaps • Statistics ofMarkovMaps • PowerSpectraofMarkovMaps • ModelingEventuallyExpandingMapswith MarkovMaps 73FractalSignals GregoryW.Wornell Introduction • FractalRandomProcesses • DeterministicFractalSignals • FractalPointProcesses 74MorphologicalSignalandImageProcessing PetrosMaragos Introduction • MorphologicalOperatorsforSetsandSignals • Median,Rank,andStackOperators • UniversalityofMorphologicalOperators • MorphologicalOperatorsandLatticeTheory • Slope Transforms • MultiscaleMorphologicalImageAnalysis • DifferentialEquationsforContinuous- ScaleMorphology • ApplicationstoImageProcessingandVision • Conclusions 75SignalProcessingandCommunicationwithSolitons AndrewC.Singer Introduction • SolitonSystems:TheTodaLattice • NewElectricalAnalogsforSolitonSystems • CommunicationwithSolitonSignals • NoiseDynamicsinSolitonSystems • EstimationofSoliton Signals • DetectionofSolitonSignals 76Higher-OrderSpectralAnalysis AthinaP.Petropulu Introduction • DefinitionsandPropertiesofHOS • HOSComputationfromRealData • Linear Processes • NonlinearProcesses • Applications/SoftwareAvailable T RADITIONALLY,SIGNALPROCESSINGasadisciplinehasreliedheavilyonatheoretical foundationoflineartime-invariantsystemtheoryinthedevelopmentofalgorithmsfora broadrangeofapplications.Inrecentyearsaconsiderablebroadeningofthistheoretical basehasbeguntotakeplace.Inparticular,therehasbeensubstantialgrowthininterestintheuse c  1999byCRCPressLLC of a variety of nonlinear systems with special properties for diverse applications. Promising new techniquesforthe synthesis andanalysis of suchsystemscontinuetoemerge. Atthesametime, there hasalso been rapidg rowth ininterestinsystemsthatarenot constrained tobetime-invariant. These may be systems that exhibit temporal fluctuations in their characteristics, or, equally importantly, systemscharacterizedbyotherinvarianceproperties,suchasinvariancetoscalechanges. Inthelatter case, this gives rise to systems with fractal characteristics. In some cases, these systems are directly applicable for implementing various kinds of signal processingoperations such as signal restoration, enhancement, or encoding, or for modeling certain kinds of distortion encountered in physical environments. In other cases, they serve as mechanisms for generating new classes of signal models for existing and emerging applications. In particular, whenautonomousordrivenbysimplerclassesofinputsignals,they generaterichclassesof signalsat theiroutputs. Inturn,thesenewclassesofsignalsgiverisetonewfamiliesofalgorithmsforefficiently exploiting them in the context of applications. Thespectrum oftechniquesfornonlinear signalprocessingisextremelybroad,and in thischapter we make no attempt to cover the entire array of exciting new directions b eing pursued within the community. Rather, we present a ver y small sampling of several highly promising and interesting ones to suggest the richness of the topic. A br ief overview of the specific chapters comprising this section is as follows. Chapters71and72discussthechaoticbehaviorofcertainnonlineardynamicalsystemsandsuggest ways in which this behavior can be exploited. In particular, Chapter 71 focuses on continuous-time chaoticsystems characterized bya special self-synchronizationproperty thatmakesthem potentially attractive for a range of secure communications applications. Chapter 72 describes a family of discrete-time nonlinear dynamical and chaotic systems that are particularly attractive for use in a variety of signal processing applications ranging from signal modeling in power converters to pseudorandom number generation and error-correctioncoding in signal transmission applications. Chapter 73 discusses fractal signals which arise out of self-similar system models characterized by scale-invariance. These represent increasingly important models for a range of natural and man- made phenomena in applications involving both signal synthesis and analysis. Multidimensional fractals also arise in thestate-spacerepresentationof chaotic signals, andthefractal propertiesin this representationareimportantintheidentification,classification,andcharacterizationofsuchsignals. Chapter 74 focuses on morphological signal processing, which encompasses an important class of nonlinear filtering techniques together with some powerful associated signal representations. Morphological signal processing is closely related to a number of classes of algorithms including order-statisticsfiltering,cellularautomatamethodsforsignalprocessing,andothers. Morphological algorithms are currently among the most successful and widely used nonlinear signal processing techniques in image processing and vision for such tasks as noise suppression, feature extraction, segmentation, and others. Chapter 75 discusses the analysis and synthesis of soliton signals and their potential use in com- munication applications. These signals arise in systems satisfying certain classes of nonlinear wave equations. Because they propagate through those equations without dispersion, there has been longstanding interest in their use as carrier waveforms over fiber-optic channels having the appro- priate nonlinear characteristics. As they propagate through these systems, they also exhibit a special type of reduced-energy superposition property that suggests an interesting multiplexing strategy for communications over linear channels. Finally, Chapter 76 discusses nonlinear representations for stochastic signals in terms of their higher-order statistics. Such representations are particularly important in the processing of non- Gaussian signals for which moretraditional second-moment characterizations are ofteninadequate. The associated tools of higher-order spectral analysis find increasing application in many signal detection, identification, modeling, and equalization contexts, where they have led to new classes of powerful signal processing algor ithms. c  1999 by CRC Press LLC Again,thesearticlesareonlyrepresentativeexamplesofthemanyemergingdirectionsinthisactive areaofresearchwithinthesignalprocessingcommunity,anddevelopmentsinmanyotherimportant and exciting directions can be found in the community’s journal and conference publications. c  1999 by CRC Press LLC . richness of the topic. A br ief overview of the specific chapters comprising this section is as follows. Chapters71and72discussthechaoticbehaviorofcertainnonlineardynamicalsystemsandsuggest ways. self-synchronizationproperty thatmakesthem potentially attractive for a range of secure communications applications. Chapter 72 describes a family of discrete-time